JEE Physics Formula Sheet

N is Newton, dyn is dyne, J is Joule, and erg is erg.

$[Q]$ represents the dimensions of physical quantity $Q$; $M, L, T, I, \theta, N, J$ are the seven fundamental dimensions.

$a_i$ is the $i$-th measurement, $a_{mean}$ is the arithmetic mean, and $\Delta a_{mean}$ is the mean absolute error.

$e_r$ represents relative error, and $e_p$ represents percentage error.

$A, B, C$ are measured quantities with errors $\Delta A, \Delta B, \Delta C$; $Z$ is the resulting calculated quantity.

$v_{avg}$ is average speed, $\vec{v}_{avg}$ is average velocity vector, $\Delta \vec{r}$ is displacement vector, and $\Delta t$ is total elapsed time.

$v_{avg}$ is the average velocity, $v_{inst}$ is the instantaneous velocity, $x$ represents position, and $t$ represents time.

$u$ is initial velocity, $v$ is final velocity, $a$ is constant acceleration, $t$ is elapsed time, $s$ is displacement, and $s_n$ is the displacement in the $n$-th second.

$v_{AB}$ is the velocity of object A relative to B, $v_A$ is the velocity of A, and $v_B$ is the velocity of B.

$R$ is magnitude of resultant vector, $A, B$ are magnitudes of the individual vectors, $\theta$ is angle between them, and $\alpha$ is angle of resultant with vector $A$.

$\vec{A}$ and $\vec{B}$ are vectors, $A$ and $B$ are their magnitudes, and $\theta$ is the angle between them.

$u$ is the launch speed, $\theta$ is the launch angle with the horizontal, $T$ is time of flight, $H$ is max height, $R$ is range, and $g$ is acceleration due to gravity.

$v$ is linear speed, $\omega$ is angular velocity, $r$ is circular radius, $f$ is frequency, $T$ is time period, and $a_c$ is centripetal acceleration.

$\vec{F}$ is force, $\vec{p}$ is linear momentum, $m$ is mass, and $\vec{a}$ is acceleration.

$\vec{p}$ is linear momentum, $m$ is mass, $\vec{v}$ is velocity, $\vec{J}$ is impulse, and $\Delta \vec{p}$ is the change in momentum.

$f_{s,max}$ is limiting static friction, $f_k$ is kinetic friction, $\mu_s$ and $\mu_k$ are coefficients of static and kinetic friction respectively, and $N$ is normal force.

$r$ is circular radius, $g$ is acceleration due to gravity, $\mu_s$ is coefficient of static friction, $\theta$ is banking angle, $v_{opt}$ is friction-free optimum speed, and $v_{max}$ is maximum safe speed.

$W$ is work done, $\vec{F}$ is force, $\vec{d}$ is constant displacement, and $d\vec{r}$ is differential displacement.

$W_{net}$ is net work done, $\Delta K$ is change in kinetic energy, $P$ is power, $\vec{F}$ is force, and $\vec{v}$ is velocity.

$F_x$ is the conservative force along the x-axis, and $U$ is the potential energy as a function of position $x$.

$U$ is the stored potential energy, $k$ is the spring constant, and $x$ is the extension or compression.

$v$ is the critical speed, $T$ is the tension in the string, $R$ is the radius of the circle, $m$ is the mass, and $g$ is the acceleration due to gravity.

$e$ is the coefficient of restitution, $u_1, u_2$ are velocities before collision, $v_1, v_2$ are velocities after collision, and $m_1, m_2$ are the colliding masses.

$\vec{r}_{cm}$ is the center of mass position vector, and $m_i$ and $\vec{r}_i$ are the mass and position of the $i$-th particle.

$\vec{r}_{cm}$ is the center of mass position vector, $M$ is total mass, and $dm$ is a differential mass element.

$\vec{\tau}$ is torque, $\vec{r}$ is position vector, $\vec{F}$ is force vector, $I$ is moment of inertia, and $\vec{\alpha}$ is angular acceleration.

$\vec{L}$ is angular momentum, $\vec{r}$ is position, $\vec{p}$ is linear momentum, $I$ is moment of inertia, $\vec{\omega}$ is angular velocity, and $\vec{\tau}_{net}$ is net torque.

$I$ is moment of inertia, $r$ represents distance from axis of rotation, $M$ is total mass, and $K$ is the radius of gyration.

$I_z$ is moment of inertia about the target axis, $I_{cm}$ is moment of inertia about parallel center-of-mass axis, $M$ is total mass, $d$ is perpendicular distance between axes, and $I_x, I_y$ are moments of inertia about perpendicular axes in the plane of a laminar sheet.

$F$ is gravitational force, $G$ is gravitational constant, $m_1, m_2$ are masses, $r$ is orbital radius, $T$ is orbital period, and $M_s$ is mass of the central star/Sun.

$g$ is gravity at sea level, $g_h$ and $g_d$ are gravity values at height $h$ and depth $d$, $R$ is Earth's radius, $\omega$ is Earth's rotational speed, and $\phi$ is the latitude.

$U$ is gravitational potential energy, $V$ is gravitational potential, $M, m$ are masses, and $r$ is the separation distance.

$v_e$ is escape velocity, $v_o$ is orbital velocity, $M$ is Earth's mass, $R$ is Earth's radius, and $g$ is acceleration due to gravity.

$F$ is applied deforming force, $A$ is cross-sectional area, $E$ is modulus of elasticity, $\Delta L$ is elongation, and $L_0$ is original length.

$Y$ is Young's Modulus, $B$ is Bulk Modulus, $F$ is stretching force, $L$ is length, $A$ is area, $\Delta L$ is extension, $\Delta P$ is pressure change, and $\Delta V$ is volume change.

$\sigma$ is Poisson's ratio (theoretical limits: $-1 \le \sigma \le 0.5$), $Y$ is Young's modulus, $B$ is Bulk modulus, and $\eta$ is Shear modulus (rigidity modulus).

$u_{energy}$ is energy density, Stress represents applied force per unit area, and Strain is fractional deformation.

$P$ is total pressure at depth $h$, $P_0$ is atmospheric pressure at surface, $\rho$ is fluid density, and $g$ is acceleration due to gravity.

$F_B$ is the buoyant force, $\rho_f$ is the density of the fluid, $V_{\text{sub}}$ is the volume of the submerged part of the body, and $g$ is the acceleration due to gravity.

$F_d$ is viscous drag, $\eta$ is coefficient of viscosity, $r$ is sphere radius, $v$ is speed, $v_t$ is terminal velocity, $\rho_{body}$ is density of sphere, and $\rho_{fluid}$ is fluid density.

$R_e$ is Reynolds number, $\rho$ is fluid density, $v$ is flow velocity, $d$ is diameter of tube, and $\eta$ is coefficient of viscosity.

$A$ represents cross-sectional area, $v$ represents flow velocity, $P$ is pressure, $h$ is height, and $\rho$ is fluid density.

$W$ is the work done (stored as surface energy), $T$ is the surface tension of the liquid, and $\Delta A$ is the increase in surface area (taking both surfaces into account for a film).

$T$ is surface tension, $R$ is radius of curved interface, and $\Delta P$ is the excess pressure.

$T$ is surface tension, $h$ is capillary height, $\theta$ is contact angle, $\rho$ is density of liquid, $g$ is acceleration due to gravity, and $r$ is tube radius.

$C$ is temperature in degrees Celsius, $F$ is in degrees Fahrenheit, and $K$ is in Kelvin.

$L$ is final length, $L_0$ is initial length, $\alpha$ is linear expansion coefficient, and $\Delta T$ is temperature change.

$Q$ is heat exchanged, $m$ is mass, $s$ is specific heat, $L$ is latent heat, and $\Delta T$ is temperature change.

$k$ is thermal conductivity, $A$ is area, $L$ is length, and $T$ is temperature.

$\lambda_{\text{max}}$ is wavelength of maximum radiation intensity, $T$ is absolute temperature, and $b$ is Wien's displacement constant ($2.898 \times 10^{-3} \text{ m K}$).

$E$ is radiative power, $\sigma$ is Stefan-Boltzmann constant, $e$ is emissivity, $A$ is area, $T$ is temperature, $\lambda_m$ is peak wavelength, and $b$ is Wien's constant.

$T$ is body temperature, $T_s$ is surrounding temperature, $K$ is positive constant, and $t$ is time.

$T_C$ is Celsius temperature, $T_F$ is Fahrenheit temperature, and $T_K$ is Kelvin (absolute) temperature.

$\Delta Q$ is heat added, $\Delta U = n C_v \Delta T$ is internal energy change, and $W$ is work.

$W$ is work, $n$ is mole count, $R$ is gas constant, $T$ is temperature, $V_i, V_f$ are volumes, $P_i, P_f$ are pressures, and $\gamma$ is adiabatic index.

$P$ is pressure, $V$ is volume, $T$ is absolute temperature, and $\gamma = C_p/C_v$ is the adiabatic index (ratio of specific heats).

$\beta$ is coefficient of performance, $Q_C$ is heat extracted from cold reservoir, $W$ is work input, $T_C$ is cold temperature, and $T_H$ is hot temperature.

$\eta$ is efficiency, $\beta_{COP}$ is coefficient of performance, $T_C$ is absolute cold reservoir temperature, and $T_H$ is absolute hot reservoir temperature.

$P$ is pressure, $V$ is volume, $n$ is moles, $T$ is temperature, $R$ is gas constant, and $W$ is work done on the gas.

$P$ is pressure, $\rho$ is density, and $v_{rms}$ is RMS molecular speed.

$v_{rms}$ is RMS speed, $M$ is molar mass, $m$ is single molecule mass, $k_B$ is Boltzmann constant, $C_v, C_p$ are specific heats, $f$ is degrees of freedom, and $R$ is gas constant.

$\lambda$ is mean free path, $d$ is collision diameter, and $n$ is number density.

$x$ is displacement, $A$ is amplitude, $\omega$ is angular frequency, $\phi$ is initial phase, $v$ is velocity, and $a$ is acceleration.

$E_{total}$ is energy, $m$ is mass, $\omega$ is angular frequency, and $A$ is amplitude.

$T$ is time period, $k$ is spring constant, $m$ is mass, $L$ is pendulum length, and $g$ is acceleration due to gravity.

$A(t)$ is damped amplitude, $A_0$ is initial amplitude, $b$ is damping constant, $m$ is mass, and $\omega'$ is the damped angular frequency.

$T$ is tension, $\mu$ is linear mass density, $\gamma$ is adiabatic index, $R$ is gas constant, $T$ is temperature, and $M$ is molar mass.

$y$ is displacement, $A$ is amplitude, $k = 2\pi/\lambda$ is wave number, $\omega = 2\pi f$ is angular frequency, $v$ represents speed, $T$ is tension, $\mu$ is linear mass density, and $\gamma$ is adiabatic index of gas.

$y$ is the displacement at position $x$ and time $t$, $A$ is the amplitude of individual waves, $k = 2\pi/\lambda$ is the wave number, and $\omega = 2\pi f$ is the angular frequency.

$f$ represents frequency, $v$ is sound velocity, and $L$ is length of pipe.

$f_{beat}$ is beat frequency, and $f_1, f_2$ are source frequencies.

$f'$ is observed frequency, $f$ is source frequency, $v$ is speed of sound in medium, $v_o$ is observer speed, and $v_s$ is source speed.

$q$ is the net charge, $n$ is any integer (positive or negative), and $e \approx 1.6 \times 10^{-19}$ C is the elementary charge of an electron.

$\vec{F}$ is force, $q_1, q_2$ are point charges, $r$ is separation distance, $\hat{r}$ is unit vector along separation line, and $\varepsilon_0$ is vacuum permittivity.

$E$ is electric field intensity, $q$ is charge magnitude, $r$ is distance, and $\varepsilon_0$ is permittivity of free space.

$p = q(2a)$ is electric dipole moment magnitude, $r$ is distance from dipole center ($r \gg a$), $E$ is electric field, and $\vec{\tau}$ is torque vector in field $\vec{E}$.

$\Phi_E$ is electric flux, $q_{en}$ is enclosed net charge, $\lambda$ is linear charge density, $\sigma$ is surface charge density, and $r$ is radial distance.

$V$ is electric potential, $q$ is charge, and $r$ is separation distance.

$U$ is electrostatic potential energy, $q_1, q_2$ are charges, and $r$ is separation distance.